CAMBRIDGE — “Brothers fight sometimes,” begins Dave Alvin’s liner notes to “Common Ground,” his new album with his brother Phil — the first they’ve recorded together since Dave left the Blasters some 30 years ago. “They argue, tease, bully, and disagree.”

It’s no secret that the Alvins have had their share of disagreements. “But brothers are always brothers,” Alvin’s notes continue, and their aptly named record, which celebrates the music of Big Bill Broonzy — what he calls their “shared musical square one” — is testament to that. Their show at The Sinclair, with snap-tight accompaniment from backing band the Guilty Ones, had the same spirit; it drew heavily on the record, added songs that focused on their musical roots, and was a giant exercise in brotherly love.

Saturday’s homage by these “little Big Bill Broonzy fans” pulled eight songs from “Common Ground,” including “All by Myself” (which kicked off the show with the Alvins trading vocals), the hard-swinging blues of “The Stuff They Call Money,” and a blistering take on “How You Want It Done,” a 1929 recording that the brothers agreed (“treasure that,” Dave quipped) is the first-ever rockabilly recording.

The Blasters had a remarkable talent for taking classic blues, R&B, and rock ’n’ roll and making it their own, and Saturday’s renditions of the Big Bill Broonzy songs were no different. Not surprisingly, there was a distinct Blasters groove to the proceedings. The brothers drew on the Blasters’ repertoire for material as well, notably a pair of songs that gave another glance back to the Alvins’ musical roots, “Border Radio” and Leiber and Stoller’s “One Bad Stud” (which, Dave noted, reminded him of the days when he and his brother were following the likes of Lee Allen and T-Bone Walker around).

As ever, younger brother Dave was the loquacious one — commenting, observing, and adding context to songs — while Phil stood and listened, occasionally nodding or smiling. When Phil opened his mouth, it was primarily to unleash his phenomenal singing voice or to play harp (something, Dave pointed out, his brother learned from blues legend Sonny Terry). Dave remarked several times on his brother’s “amazing” voice (they weren’t the Everly Brothers, he noted wryly; the deal in the Blasters was that he wrote the songs and his brother sang them). Nowhere was that more evident than on a cover of an early James Brown tune, “Please, Please, Please,” that Phil absolutely ignited with his pleading intensity.

The Alvins also played “What’s Up With Your Brother,” Dave’s tongue-in-cheek song from a couple years back referencing their troubles. But Saturday’s show made plain that these days both are delighted with what’s up: one brother standing and playing next to the other.